Related papers: On Delisle's geographical projection
``In this paper we give the history of Leonhard Euler's work on the pentagonal number theorem, and his applications of the pentagonal number theorem to the divisor function, partition function and divergent series. We have attempted to give…
Deflection of light due to massive objects was predicted by Einstein in his General Theory of Relativity. This deflection of light has been calculated by many researchers in past, for spherically symmetric objects. But, in reality, most of…
Almost all the "Voyages Extraordinaires" written by Jules Verne refer to astronomy. In some of them, astronomy is even the leading theme. However, Jules Verne was basically not learned in science. His knowledge of astronomy came from…
Euler observers are a fundamental tool for the study of spacetime evolution. Cauchy surfaces are evolved through the use of hypersurface orthogonal fields and their relationship to coordinate observers, that enable the use of already…
The following translation of Leonhard Euler's "Examination of an Artifice for Propelling a Ship by the Principle of Internal Motion," originally published in 1750, offers a glimpse into a fascinating historical debate in the field of…
This article provides a historical overview of Geometry of Numbers. 1. Figures, 2. The circuit problem and its relatives, 3. Minkowski lattice point set, 4. The young Hermann Minkowski, 5. The geometry of numbers develops, 6. Minkowski…
The Euclid mission aims to measure the positions, shapes, and redshifts of over a billion galaxies to provide unprecedented constraints on the nature of dark matter and dark energy. Achieving this goal requires a continuous reassessment of…
This is an attempt to present axioms for Euclidean geometry, aiming at the following goals: to work with geometric notions (thus not merely identify points with pairs of numbers, giving a special status to a particular coordinate system);…
The year 2012 will be the fourth centennial year of the Jesuit Christopher Clavius (1535-1612), known as the Euclid of XVI century and the collaborator of the Pope Gregory XIII for the calendar reformation. In the occasion of the year of…
Both lectures focus on the first part of the so-called 'mathematical part' of Plato's Theaetetus. In this passage, the young Theaetetus briefly recounts the mathematical lesson given by the geometer Theodorus. The first lecture delves into…
Frederick William Gehring was a hugely influential mathematician who spent most of his career at the University of Michigan. Gehring's major research contributions were to Geometric Function Theory, particularly in higher dimensions…
This paper investigates the relationship between a system of differential equations and the underlying geometry associated with it. The geometry of a surface determines shortest paths, or geodesics connecting nearby points, which are…
Euclidean geometry is among the earliest forms of mathematical thinking. While the geometric primitives underlying its constructions, such as perfect lines and circles, do not often occur in the natural world, humans rarely struggle to…
The first paper in systolic geometry was published by Loewner's student P. M. Pu over half a century ago. Pu proved an inequality relating the systole and the area of an arbitrary metric on the real projective plane. We prove a stronger…
This is an expository article for Elsevier's Encyclopedia of Mathematical Physics on the subject in the title. Comments/corrections welcome.
A few thoughts on physical meaning of geometry, space and time.
Given a set of points in the Euclidean space $\mathbb{R}^\ell$ with $\ell>1$, the pairwise distances between the points are determined by their spatial location and the metric $d$ that we endow $\mathbb{R}^\ell$ with. Hence, the distance…
The classification of algebraic surfaces by the Italian School of algebraic geometry is universally recognized as a breakthrough in 20th-century mathematics. The methods by which it was achieved do not, however, meet the modern standard of…
The problem of mathematical modeling in geography is one of the most important strategies in order to establish the evolution and the prevision of geographical phenomena. Models must have a simplified structure, to reflect essential…
This book intends to give the main definitions and theorems in mathematics which could be useful for workers in theoretical physics. It gives an extensive and precise coverage of the subjects which are addressed, in a consistent and…